Question

J&J has an outstanding issue of 20- year maturity bond with face value of $1,000 and a coupon of 8%, paying coupon interest semi-annually. If the market price of this bond is $1200, what is the rate of return investors are demanding on this bond?

Answer 1

Here we need to compute the YTM of the bond

Par Value of the bond = $1000

Current price of the bond = $1200

Annual coupon rate of the bond = 8%

Annual coupon payment = Annual coupon rate*Face Value = 8%*1000 = 80

Time to maturity in years = 20 years

It is given that the bond makes semiannual payments. Hence we will consider semiannual coupon payments and time to maturity in semiannual periods

Semi-annual coupon payment = Annual coupon payment/2 = 80/2 = 40

Time to maturity in semiannual periods = 20*2 = 40

Method 1: YTM calculation using ba ii plus calculator

Input the following values in ba ii plus calculator

N = 40

PV = -1200

PMT = 40

FV = 1000

CPT -> I/Y [Press CPT and then press I/Y]

We get, I/Y =3.11814976

Note that this is semi-annual YTM as we have taken semi-annual coupons and time to maturity in semiannual periods. To convert semi-annual YTM into annual YTM we need to multiply it by 2.

Annual YTM = 3.11814976%*2 =6.23629952% ~ 6.24% (Rounded to two decimals)

YTM = 6.24%

Answer -> 6.24%

Method 2: YTM Calculation using Excel

We can compute the semi-annual YTM using RATE function in Excel as shown below:

=RATE(40,40,-1200,1000) = 3.12%

Note that this is the semiannual YTM. We will convert it to annual YTM by multiplying it by 2

Annual YTM = 3.12%*2 = 6.24%

Return demanded by investors = YTM = 6.24%

Answer -> 6.24%